Solve x^2*.309=3.2

$${ x }^{ 2 } \times .309=3.2$$

Solve for x

$$x = \frac{40 \sqrt{618}}{309} \approx 3.218071947$$

$$x = -\frac{40 \sqrt{618}}{309} \approx -3.218071947$$

Steps by Finding Square Root

Divide both sides by 0.309.

$$x^{2}=\frac{3.2}{0.309}$$

Expand \frac{3.2}{0.309} by multiplying both numerator and the denominator by 1000.

$$x^{2}=\frac{3200}{309}$$

Take the square root of both sides of the equation.

$$x=\frac{40\sqrt{618}}{309} x=-\frac{40\sqrt{618}}{309}$$

Steps Using the Quadratic Formula

Divide both sides by 0.309.

$$x^{2}=\frac{3.2}{0.309}$$

Expand \frac{3.2}{0.309} by multiplying both numerator and the denominator by 1000.

$$x^{2}=\frac{3200}{309}$$

Subtract \frac{3200}{309} from both sides.

$$x^{2}-\frac{3200}{309}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -\frac{3200}{309} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-\frac{3200}{309}\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-\frac{3200}{309}\right)}}{2}$$

Multiply -4 times -\frac{3200}{309}.

$$x=\frac{0±\sqrt{\frac{12800}{309}}}{2}$$

Take the square root of \frac{12800}{309}.

$$x=\frac{0±\frac{80\sqrt{618}}{309}}{2}$$

Now solve the equation x=\frac{0±\frac{80\sqrt{618}}{309}}{2} when ± is plus.

$$x=\frac{40\sqrt{618}}{309}$$

Now solve the equation x=\frac{0±\frac{80\sqrt{618}}{309}}{2} when ± is minus.

$$x=-\frac{40\sqrt{618}}{309}$$

The equation is now solved.

$$x=\frac{40\sqrt{618}}{309} x=-\frac{40\sqrt{618}}{309}$$